A direct comparison of high-speed methods for the numerical Abel transform

The Abel transform is a mathematical operation that transforms a cylindrically symmetric three-dimensional (3D) object into its two-dimensional (2D) projection. The inverse Abel transform reconstructs the 3D object from the 2D projection. Abel transforms have wide application across numerous fields of science, especially chemical physics, astronomy, and the study of laser-plasma plumes. Consequently, many numerical methods for the Abel transform have been developed, which makes it challenging to select the ideal method for a specific application. In this work eight transform methods have been incorporated into a single, open-source Python software package (PyAbel) to provide a direct comparison of the capabilities, advantages, and relative computational efficiency of each transform method. Most of the tested methods provide similar, high-quality results. However, the computational efficiency varies across several orders of magnitude. By optimizing the algorithms, we find that some transform methods are sufficiently fast to transform 1-megapixel images at more than 100 frames per second on a desktop personal computer. In addition, we demonstrate the transform of gigapixel images.Comment: 9 pages, 5 figure

Scale Stain: Multi-Resolution Feature Enhancement in Pathology Visualization

Digital whole-slide images of pathological tissue samples have recently become feasible for use within routine diagnostic practice. These gigapixel sized images enable pathologists to perform reviews using computer workstations instead of microscopes. Existing workstations visualize scanned images by providing a zoomable image space that reproduces the capabilities of the microscope. This paper presents a novel visualization approach that enables filtering of the scale-space according to color preference. The visualization method reveals diagnostically important patterns that are otherwise not visible. The paper demonstrates how this approach has been implemented into a fully functional prototype that lets the user navigate the visualization parameter space in real time. The prototype was evaluated for two common clinical tasks with eight pathologists in a within-subjects study. The data reveal that task efficiency increased by 15% using the prototype, with maintained accuracy. By analyzing behavioral strategies, it was possible to conclude that efficiency gain was caused by a reduction of the panning needed to perform systematic search of the images. The prototype system was well received by the pathologists who did not detect any risks that would hinder use in clinical routine